Consider a code with five valid code words of length ten : 0000000000,…
2014
Consider a code with five valid code words of length ten :
0000000000, 0000011111,
1111100000, 1110000011,
1111111111
Hamming distance of the code is
- A.
5
- B.
10
- C.
4
- D.
9
Attempted by 406 students.
Show answer & explanation
Correct answer: C
Key idea: the Hamming distance of a code is the smallest Hamming distance between any two distinct codewords.
Given codewords:
0000000000
0000011111
1111100000
1110000011
1111111111
Check the pair that gives the smallest distance:
Compare 1111100000 and 1110000011: they are identical in positions 1–3 and 6–8, but differ in positions 4, 5, 9, and 10.
Therefore their Hamming distance is 4.
Conclusion: the Hamming distance of the code is 4.